Math ChampionsDay 1

A championship team is a team of champions.

- Unknown

BLOG - math.commons.hwdsb.on.caTwitter - #hwdsbmathstrategy

Agenda1. What is a Mathematical Thinker?2. Refining our Thinking …. on Thinking3. What is Inquiry?4. How does Inquiry support our Professional Learning in Mathematics?5. Supporting Students to Become Better Thinkers through Teacher Inquiry6. Determining Focus7. Next Steps

Seven Norms of Collaboration

• Presuming positive intentions• Promoting a spirit of inquiry• Pausing• Paraphrasing• Probing• Putting forward ideas• Paying attention to self and others

Minds On

Which picture below represents math instruction in your classroom and why? Share in your table groups.

What is Thinking in Mathematics?Chalk Talk

Silent Activity1. Respond to the question without talking2. Extend the ideas of others; draw connecting lines; add your idea to theirsNow 3. Walk around and look at ideas from other groups. 4. Add your ideas.

Thinking - The Achievement ChartThinking is…• The use of critical and creative thinking skills and/or

processes, as follows:▫ Planning skills (e.g. understanding the problem, making a plan for

solving for problem)▫ Processing skills (e.g. carrying out a plan, looking back at the

solution)▫ Critical/creative thinking processes (e.g. inquiry, problem solving)

The Ontario Mathematics Curriculum, Grades 1-8, 2005

Thinking - EQAO

Thinking (TH)Students are required to select and sequence a variety of tools to solve a problem and demonstrate a critical-thinking process.

To answer the question, students need to make a plan.

EQAO, 2013

Refining our Thinking…on Thinking

Why the focus on Thinking in HWDSB?

● Focus on the thinking process versus product

● Thinking is across all the strands● Real life applications ● EQAO trends

Why Thinking in Mathematics?Students who are “thinkers” in mathematics develop…

• Deeper engagement and understanding; learning through inquiry

• Greater independence and self-regulation; constructing their thinking

• Stronger competence with mathematical processes; problem solving, reasoning, representing and communicating

Critical Thinking in Mathematics: What? Why? When? And How? 2013

Characteristics/Attributes of Thinking in Mathematics How do you know?

Thinking in MathematicsCharacteristics/Attributes Evidence (How do you know?)

BEGIN TO THINK ABOUT THE EVIDENCE LISTED AND ADD ADDITIONAL

EVIDENCE

BEGIN WITH THE EXAMPLES ON THE

PAGE AND ADD YOUR OWN IDEAS

Introduction to Teacher Inquiry

The essence of inquiry …

“Inquiry...requires more than simply answering questions or getting a right answer. It espouses investigation, exploration, search, quest, research, pursuit, and study. It is enhanced by involvement with a community of learners, each learning from the other in social interaction.”

Kuklthau, Maniotes & Caspari, 2007, p. 2

Getting Started with Teacher Inquiry

Video

• Individually think about your top three student needs in thinking in mathematics based on the Characteristics/Attributes Chart

Now..• As a table group, list the top three student

needs about Thinking in Mathematics

Getting Started with Teacher Inquiry about Thinking in Mathematics

Getting Started with

Teacher Inquiry about

Thinking in Mathematics

Characteristics of Rich Tasks

Adapted from Eric Hsu, Judy Kysh, and Diane Resek. Revitalizing Algebra (REAL), NSF Mathematics/Science Partnership Project

● Mystery in task -- not just larger numbers● Task requires a plan● Multiple entry points● Aligned to the intention of the curriculum

expectation

Which task(s) encourage thinking? Justify your thinking.

A RichTask

1. Can two coins be worth more than five coins? How do you know?

2. 10 cents + 2 cents = ?

3. I have 45 cents in my pocket, which coins could I have? Show your work.

Curriculum Expectation: Grade 2 NSN - Operational Sense (OE3) – add and subtract money amounts to 100¢ using a variety of tools and strategies

Exploring Thinking: 3 StationsEliciting, developing and constructing student thinking using:

Manipulatives Discourse & Accountable

Talk

Questioning & Feedback

Developing your Inquiry• As a group you will

• decide on one area of focus (The Task, Accountable Talk/Discourse, Manipulatives or Questioning/Feedback)

• create an “if...then” statement• list evidence of impact on student achievement

• Between now and session 2 • begin your inquiry based on your if/then statement • collect evidence• document your learning (with support by Instructional Coach)

• Bring to session 2• your learning• your evidence

Examples:

If I ask questions that promote thinking then my students will be able to justify their responses.

If I create opportunities for students to engage in accountable talk then my students will be able to communicate their strategies and/or solutions.

IF…. (Teacher action) THEN … (Evidence)

What is the Evidence of Impact?• As a team, brainstorm the evidence of

impact for your focus.

• Use the ideas created at your table earlier, as well as any additional ideas from visiting the station sessions.

Developing your Inquiry• As a group you will

• decide on one area of focus (Accountable Talk/Discourse, Manipulatives or Questioning/Feedback)

• create an “if...then” statement• list evidence of impact on student achievement

• Between now and session 2 • begin your inquiry based on your if/then statement • collect evidence• document your learning (with support by Instructional Coach)

• Bring to session 2• your learning• your evidence

Next Steps TODAY● Choose the date and location for Day 2 (by the end of February)

IN BETWEEN Day 1 and Day 2● Document the journey (collect evidence) and refine focus, if necessary

DAY 2● Bring evidence of the journey (student work and learnings)